Factor by Grouping (x+3)^2+14(x+3)+49

${(x + 3)}^{2} + 14 (x + 3) + 49$

Step 1

Simplify each term.

Rewrite ${(x + 3)}^{2}$ as $(x + 3) (x + 3)$ .

$(x + 3) (x + 3) + 14 (x + 3) + 49$

Expand $(x + 3) (x + 3)$ using the FOIL Method.

Apply the distributive property.

$x (x + 3) + 3 (x + 3) + 14 (x + 3) + 49$

Apply the distributive property.

$x \cdot x + x \cdot 3 + 3 (x + 3) + 14 (x + 3) + 49$

Apply the distributive property.

$x \cdot x + x \cdot 3 + 3 x + 3 \cdot 3 + 14 (x + 3) + 49$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 3 + 3 x + 3 \cdot 3 + 14 (x + 3) + 49$

Move $3$ to the left of $x$ .

$x^{2} + 3 \cdot x + 3 x + 3 \cdot 3 + 14 (x + 3) + 49$

Multiply $3$ by $3$ .

$x^{2} + 3 x + 3 x + 9 + 14 (x + 3) + 49$

Add $3 x$ and $3 x$ .

$x^{2} + 6 x + 9 + 14 (x + 3) + 49$

Apply the distributive property.

$x^{2} + 6 x + 9 + 14 x + 14 \cdot 3 + 49$

Multiply $14$ by $3$ .

$x^{2} + 6 x + 9 + 14 x + 42 + 49$

Step 2

Simplify by adding terms.

Add $6 x$ and $14 x$ .

$x^{2} + 20 x + 9 + 42 + 49$

Simplify by adding numbers.

Add $9$ and $42$ .

$x^{2} + 20 x + 51 + 49$

Add $51$ and $49$ .

$x^{2} + 20 x + 100$

Step 3

Factor using the perfect square rule.

Rewrite $100$ as $10^{2}$ .

$x^{2} + 20 x + 10^{2}$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$20 x = 2 \cdot x \cdot 10$

Rewrite the polynomial.

$x^{2} + 2 \cdot x \cdot 10 + 10^{2}$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = 10$ .

${(x + 10)}^{2}$